Question

explain 4 modeling with polynomials
read the section below and complete the following activity.
as seen in the previous example, polynomials can be used to model rectangles. sometimes before adding polynomials, you may need to consider the relationship between the polynomials. when working with perimeter problems, recall that the perimeter is the sum of all side lengths. therefore, to find the perimeter, you must add the length twice and the width twice.
example
model the situation with the sum of polynomials. simplify their sum.
a. rebecca is building a rectangular pen for her rabbits. the polynomial 4n + 8 represents the length of the rabbit pen, and the polynomial 2n + 6 represents the width of the rabbit pen. write a polynomial that represents the perimeter of the rabbit pen.
(2n + 6)+(2n + 6)+(4n + 8)+(4n + 8)
use a plus (+) sign to add the polynomials.
2n + 6+2n + 6+4n + 8+4n + 8
remove the parenthesis.
(2n + 2n + 4n + 4n)+(6 + 6+8 + 8)
group like terms together.
12n + 28
combine like terms. write in standard form.
the perimeter of the rabbit pen is modeled by the polynomial 12n + 28
model the situation with the sum of polynomials. write in simplest form.

1. a rectangular picture frame has the dimensions shown in the figure. write a polynomial that represents the perimeter of the frame.

Explanation:

Step1: Set up the perimeter formula

$(3x + 1)+(3x + 1)+(5x - 2)+(5x - 2)$

Step2: Remove parentheses

$3x + 1+3x + 1+5x - 2+5x - 2$

Step3: Group like - terms

$(3x+3x + 5x+5x)+(1 + 1-2 - 2)$

Step4: Combine like - terms

$16x - 2$

Answer:

$16x - 2$